Whakaoti i te -k/x^2dx=mvdv

$$- \frac { k } { x ^ { 2 } } d x = m v d v$$

Whakaoti mō d (complex solution)

$$\left\{\begin{matrix}d=0\text{, }&x\neq 0\\d\in \mathrm{C}\text{, }&k=-mxv^{2}\text{ and }x\neq 0\end{matrix}\right.$$

Ngā Upane mō te Whakaoti Whārite Rārangi

Whakareatia ngā taha e rua o te whārite ki te x^{2}.

$$\left(-\frac{k}{x^{2}}\right)dxx^{2}=mvdvx^{2}$$

Hei whakarea i ngā pū o te pūtake kotahi, me tāpiri ō rātou taupū. Tāpiria te 1 me te 2 kia riro ai te 3.

$$\left(-\frac{k}{x^{2}}\right)dx^{3}=mvdvx^{2}$$

Whakareatia te v ki te v, ka v^{2}.

$$\left(-\frac{k}{x^{2}}\right)dx^{3}=mv^{2}dx^{2}$$

Tuhia te \left(-\frac{k}{x^{2}}\right)d hei hautanga kotahi.

$$\frac{-kd}{x^{2}}x^{3}=mv^{2}dx^{2}$$

Tuhia te \frac{-kd}{x^{2}}x^{3} hei hautanga kotahi.

$$\frac{-kdx^{3}}{x^{2}}=mv^{2}dx^{2}$$

Me whakakore tahi te x^{2} i te taurunga me te tauraro.

$$-dkx=mv^{2}dx^{2}$$

Tangohia te mv^{2}dx^{2} mai i ngā taha e rua.

$$-dkx-mv^{2}dx^{2}=0$$

Whakaraupapatia anō ngā kīanga tau.

$$-dmv^{2}x^{2}-dkx=0$$

Pahekotia ngā kīanga tau katoa e whai ana i te d.

$$\left(-mv^{2}x^{2}-kx\right)d=0$$

Whakawehe 0 ki te -mv^{2}x^{2}-kx.

$$d=0$$

Whakaoti mō k (complex solution)

$$\left\{\begin{matrix}k=-mxv^{2}\text{, }&x\neq 0\\k\in \mathrm{C}\text{, }&d=0\text{ and }x\neq 0\end{matrix}\right.$$

Ngā Upane mō te Whakaoti Whārite Rārangi

Whakareatia ngā taha e rua o te whārite ki te x^{2}.

$$\left(-\frac{k}{x^{2}}\right)dxx^{2}=mvdvx^{2}$$

Hei whakarea i ngā pū o te pūtake kotahi, me tāpiri ō rātou taupū. Tāpiria te 1 me te 2 kia riro ai te 3.

$$\left(-\frac{k}{x^{2}}\right)dx^{3}=mvdvx^{2}$$

Whakareatia te v ki te v, ka v^{2}.

$$\left(-\frac{k}{x^{2}}\right)dx^{3}=mv^{2}dx^{2}$$

Tuhia te \left(-\frac{k}{x^{2}}\right)d hei hautanga kotahi.

$$\frac{-kd}{x^{2}}x^{3}=mv^{2}dx^{2}$$

Tuhia te \frac{-kd}{x^{2}}x^{3} hei hautanga kotahi.

$$\frac{-kdx^{3}}{x^{2}}=mv^{2}dx^{2}$$

Me whakakore tahi te x^{2} i te taurunga me te tauraro.

$$-dkx=mv^{2}dx^{2}$$

He hanga arowhānui tō te whārite.

$$\left(-dx\right)k=dmv^{2}x^{2}$$

Whakawehea ngā taha e rua ki te -dx.

$$\frac{\left(-dx\right)k}{-dx}=\frac{dmv^{2}x^{2}}{-dx}$$

Mā te whakawehe ki te -dx ka wetekia te whakareanga ki te -dx.

$$k=\frac{dmv^{2}x^{2}}{-dx}$$

Whakawehe mv^{2}dx^{2} ki te -dx.

$$k=-mxv^{2}$$

Whakaoti mō d

$$\left\{\begin{matrix}d=0\text{, }&x\neq 0\\d\in \mathrm{R}\text{, }&k=-mxv^{2}\text{ and }x\neq 0\end{matrix}\right.$$

Ngā Upane mō te Whakaoti Whārite Rārangi

Whakareatia ngā taha e rua o te whārite ki te x^{2}.

$$\left(-\frac{k}{x^{2}}\right)dxx^{2}=mvdvx^{2}$$

Hei whakarea i ngā pū o te pūtake kotahi, me tāpiri ō rātou taupū. Tāpiria te 1 me te 2 kia riro ai te 3.

$$\left(-\frac{k}{x^{2}}\right)dx^{3}=mvdvx^{2}$$

Whakareatia te v ki te v, ka v^{2}.

$$\left(-\frac{k}{x^{2}}\right)dx^{3}=mv^{2}dx^{2}$$

Tuhia te \left(-\frac{k}{x^{2}}\right)d hei hautanga kotahi.

$$\frac{-kd}{x^{2}}x^{3}=mv^{2}dx^{2}$$

Tuhia te \frac{-kd}{x^{2}}x^{3} hei hautanga kotahi.

$$\frac{-kdx^{3}}{x^{2}}=mv^{2}dx^{2}$$

Me whakakore tahi te x^{2} i te taurunga me te tauraro.

$$-dkx=mv^{2}dx^{2}$$

Tangohia te mv^{2}dx^{2} mai i ngā taha e rua.

$$-dkx-mv^{2}dx^{2}=0$$

Whakaraupapatia anō ngā kīanga tau.

$$-dmv^{2}x^{2}-dkx=0$$

Pahekotia ngā kīanga tau katoa e whai ana i te d.

$$\left(-mv^{2}x^{2}-kx\right)d=0$$

Whakawehe 0 ki te -mv^{2}x^{2}-kx.

$$d=0$$

Whakaoti mō k

$$\left\{\begin{matrix}k=-mxv^{2}\text{, }&x\neq 0\\k\in \mathrm{R}\text{, }&d=0\text{ and }x\neq 0\end{matrix}\right.$$

Ngā Upane mō te Whakaoti Whārite Rārangi

Whakareatia ngā taha e rua o te whārite ki te x^{2}.

$$\left(-\frac{k}{x^{2}}\right)dxx^{2}=mvdvx^{2}$$

Hei whakarea i ngā pū o te pūtake kotahi, me tāpiri ō rātou taupū. Tāpiria te 1 me te 2 kia riro ai te 3.

$$\left(-\frac{k}{x^{2}}\right)dx^{3}=mvdvx^{2}$$

Whakareatia te v ki te v, ka v^{2}.

$$\left(-\frac{k}{x^{2}}\right)dx^{3}=mv^{2}dx^{2}$$

Tuhia te \left(-\frac{k}{x^{2}}\right)d hei hautanga kotahi.

$$\frac{-kd}{x^{2}}x^{3}=mv^{2}dx^{2}$$

Tuhia te \frac{-kd}{x^{2}}x^{3} hei hautanga kotahi.

$$\frac{-kdx^{3}}{x^{2}}=mv^{2}dx^{2}$$

Me whakakore tahi te x^{2} i te taurunga me te tauraro.

$$-dkx=mv^{2}dx^{2}$$

He hanga arowhānui tō te whārite.

$$\left(-dx\right)k=dmv^{2}x^{2}$$

Whakawehea ngā taha e rua ki te -dx.

$$\frac{\left(-dx\right)k}{-dx}=\frac{dmv^{2}x^{2}}{-dx}$$

Mā te whakawehe ki te -dx ka wetekia te whakareanga ki te -dx.

$$k=\frac{dmv^{2}x^{2}}{-dx}$$

Whakawehe mv^{2}dx^{2} ki te -dx.

$$k=-mxv^{2}$$